Abstract
The coherent synchrotron radiation of a bunch in a bunch compressor may lead to the microwave instability producing longitudinal modulation of the bunch with wavelengths small compared to the bunch length. It can also be a source of an undesirable emittance growth in the compressor. We derive and analyze the equation that describes linear evolution of the microwave modulation taking into account incoherent energy spread and finite emittance of the beam. Numerical solution of this equation for the Linac Coherent Light Source bunch compressor gives the amplification factor for different wavelengths of the beam microbunching.
Highlights
The design of a magnetic bunch compressor chicane is a key technical challenge in the development of linac driven x-ray free-electron lasers
As was pointed out in Ref. [3], coherent synchrotron radiation (CSR) can be a source of modulation of the beam density at wavelengths small compared to the bunch length
In this paper we developed a linear theory describing self-induced microbunching of a beam in a magnetic bunch compressor
Summary
The design of a magnetic bunch compressor chicane is a key technical challenge in the development of linac driven x-ray free-electron lasers. The beam in the chicane can radiate coherently if the wavelength of the radiation exceeds the length of the bunch This radiation results in an undesirable growth of the beam emittance [1], which can, be cured (at least partially) by a special design of the compressor [2]. [3], coherent synchrotron radiation (CSR) can be a source of modulation of the beam density at wavelengths small compared to the bunch length. It is necessary to take into account the radial degrees of freedom since the variation of the path length with energy in the chicane results from the transverse dispersion of the trajectory. The equilibrium distribution function of the beam with the energy chirp is introduced in Sec. III as a solution of the Vlasov equation. Where x0, u0, and z0 are constants given by initial conditions, bsε ws is the beta function, b0 is the initial value of the beta function at the entrance to the compressor, b0 b0͒, as 2͑1͞2͒dbds, Dsis the dispersion function, D0͑s dDds, and wsand Dssatisfy the following equations: w00
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